Problem: Solve for $x$. Enter the solutions from least to greatest. $2x^2 - 2x - 180 = 0$ $\text{lesser }x = $
Explanation: $\begin{aligned} 2x^2 - 2x - 180 &= 0 \\\\ 2(x^2-1x-90)&=0 \end{aligned}$ Now let's factor the expression in the parentheses. $x^2-1x-90$ can be factored as $(x+9)(x-10)$. $\begin{aligned} 2(x+9)(x-10)&=0 \\\\ x+9=0&\text{ or }x-10=0 \\\\ x=-9&\text{ or }x=10 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= -9 \\\\ \text{greater }x &= 10 \end{aligned}$